Need help with $3$ Coupled ODE Dynamics question.

Question $8$

What is the first mode of vibration, i$.$e$.,$ what ratio of displacements of $x_1,x_2,$ and $x_3$ do you

need to excite the first mode of vibration?

Question $9$

What is the second mode of vibration, i$.$e$.,$ what ratio of displacements of $x_1,x_2,$ and $x_3$ do

you need to excite the second mode of vibration?

Question $10$

What is the third mode of vibration, i$.$e$.,$ what ratio of displacements of $x_1,x_2,$ and $x_3$ do you

need to excite the third mode of vibration?

$[1,1,1]$

$[1,-1\mathrm{.}414,1]$

$1,0,-1$

$[1,1\mathrm{.}414,1]$